# Radiowave Propagation - Diffraction Over Two Successive Obstructions

Author: R.J.Edwards G4FGQ © 20th August 2001This program calculates the overall transmitter-to-receiver loss when the radio path includes diffraction over two successive obstructions. Results include field strength at the receiving site. Antenna efficiency can be allowed for.

The two obstructions could be two mountain ranges or the two edges of the flat roof of a building block. Earth curvature is not taken into account.

For zero diffraction loss the direct line of sight paths between transmitter and receiver must clear the obstruction by several wavelengths. When the direct path just grazes the obstruction diffraction loss is exactly 6 dB. This program ignores the small oscillations in loss as the direct ray begins to clear an obstruction.

Diffraction loss is least when the top of the obstruction is a sharp edge. As the top becomes more rounded, i.e., as the radius of curvature increases relative to wavelength a small additional loss occurs but the program ignores this.

If the radius of curvature exceeds the height of an obstruction, or if a ridge has an irregular top edge, predicting uncertainty increases but computed overall path loss in dB can be considered to be an average or most likely value.

The transmitting and receiving antennas are located just above a flat Earth. A triangle is formed with its base on the flat Earth between transmitter and receiver and its apex at the top of one of the obstructions. A similar triangle is formed with its base on the flat Earth and its apex at the top of the other obstruction.

When the top of an obstruction protrudes above the sloping side of the triangle formed by the other obstruction then both obstructions are effective. If one of the obstructions is ineffective the program continues to compute the path loss due to the other. (*But it is easier to use Diffrac1 for only one obstruction.*)

When both obstructions are effective, three line-of-sight paths are involved:- Transmitter to Apex 1, Apex 1 to Apex 2, Apex 2 to receiver. The total transmitter to receiver path loss is the sum of the three individual path losses plus the refraction loss over each of the two obstructions plus antenna gains and/or losses.

The triangles are defined by the three line-of-sight path lengths in kilometres and heights of the two obstructions in metres above a flat Earth. The range in path lengths extends down to a few metres and obstruction heights extend down to a few tenths of a metre. Take care with measurement units.

Diffraction loss is a function of the angular change in direction as the ray passes over an obstruction. The change in angle is displayed for interest.

It is assumed the heights and widths of obstructions are not less than an order of magnitude greater than the free-space wavelength.

Depending on type of terrain, it may occur that path loss over obstructions is less than the groundwave loss which would occur if obstructions were removed. This can occur when ground conductivity is poor. Program *GrndWav3* predicts loss along groundpaths for such comparisons.

Note that when the elevation angle from an antenna to an obstruction is not too large, e.g., less than 30 degrees, the difference between slant-path distance and horizontal distance is small. The program user may enter whichever value he has knowledge of without introducing a significant error in overall propagation loss.

A "matched receiver" is one with its input resistance matched to the antenna's radiation resistance such that maximum power is transferred. Maximum receiver input power is then 50 percent of the total power available to the antenna. The other 50 percent is re-radiated.

Both transmitting and receiving antennas are isotropic except that if loss or gain relative to isotropic is known in the direction or elevation of interest it can be entered in the program.

If antenna power gain is not known enter 1. Computed results are then average values of random directivity in both the vertical and horizontal planes. This crude manner of analysis might be appropriate when a transmitter's primary service area is contained within the range of any obstructions but an average sort of value for the signal strength on the far side of obstructions may be of interest. Such distant signals may cause interference in the service areas of other transmitters and should be taken into account during planning.

When the angle between the rays on either side of the apex of an obstruction is 0 degrees the straight-line direct path just grazes the apex and diffraction loss is 6dB. Negative angles are imaginary but diffraction effects do not fall to zero until the straight line direct path runs well above the obstruction.

At very low elevation angles, long path lengths and low obstruction heights, due to ground undulations the direct rays may be indistinguishable from groundwaves and the program may underestimate total path loss. Actual loss will be intermediate between the value computed by this program and that predicted by *GrndWav3*.

Run this Program from the Web or Download and Run it from Your Computer

This program is self-contained and ready to use. It does not require installation. Click this link Diffrac2 then click *Open* to run from the web or *Save* to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer *(Right-click Start then left-click Explore to start Windows Explorer)* and it will run.

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